Spherical parts or partly spherical parts, such as a ball of a bearing, a reference sphere used as a standard in a measurement device, and a lens are widely used in an industrial field. In order to measure the shapes of these spherical parts, a number of surface shape measurement methods and devices are proposed. An interferometer device, which is a representative example thereof, can measure the surface shapes of the spherical parts with high accuracy and high density. Furthermore, for the purpose of measuring the shape of a spherical surface that is out of a surface area measurable by the surface shape measurement device, U.S. Pat. No. 6,956,657 B2 (hereinafter called Patent Literature 1) and “sphericity measurement using stitched interferometry” proceedings of JSPE autumn meeting, 2011, p. 868-869 (hereinafter called Non-Patent Literature 1) propose an apparatus that includes surface shape measurement unit and measurement position change mechanism for holding the spherical surface and changing a measurement position.
In such an apparatus, while the measurement position change mechanism changes the measurement position by shifting the spherical surface, the surface shape measurement unit measures the shapes of a plurality of partial areas. By joining the measured shapes of the plurality of partial areas by a computation called stitching, the shape of the wide spherical surface is measured.
A summary of the spherical shape measurement apparatus described in Non-Patent Literature 1 will be explained. FIG. 1 is a side view showing the structure of the apparatus. The spherical shape measurement apparatus includes a part of a laser interferometer 20 being the surface shape measurement unit, for example, a Fizeau interferometer, and a part of a measurement position change mechanism 40 being the measurement position change mechanism. The laser interferometer 20 used in this apparatus is a device that measures the surface shape of a sphere 10 by using a reference spherical surface 22 having a spherical shape and comparing the wavelength of laser light 26 generated by a laser light source 24, which is used as a yardstick, with the reference spherical surface 22. In the drawings, a reference numeral 28 refers to a beam splitter. A reference numeral 30 refers to a collimator lens for making the laser light 26 into parallel rays. A reference numeral 32 refers to an image sensor for detecting interference light synthesized by the beam splitter 28.
The sphere 10 (hereinafter simply called sphere) is disposed in a focal point of the reference spherical surface 22. Since an area measured by the laser interferometer 20 is a part of the surface of the sphere 10 to which the laser light 26 is applied, it is required to provide unit for moving the position of the laser interferometer 20 itself or the sphere 10, for the purpose of measuring a wider area. The apparatus described in Non-Patent Literature 1, which measures the shape of a sphere having a shaft, such as the sphere 10 having a support shaft 12 fixed thereto, is provided with the measurement position change mechanism 40 for moving an arbitrary surface of the sphere 10 to a measurement area of the laser interferometer 20 by a biaxial rotation mechanism having a θ rotation shaft 42 and a ϕ rotation shaft 44 orthogonal to the θ rotation shaft 42, while holding the sphere 10 through the support shaft 12.
FIG. 2 is a top plan view of the apparatus according to Non-Patent Literature 1. The ϕ rotation shaft 44 is adjusted so as to form a right angle with a measurement optical axis (perpendicular direction in the drawing of FIG. 2) and coincide with the focal point of the reference spherical surface 22 positioned thereon. By rotating the ϕ rotation shaft 44, a bracket 46 for supporting the θ rotation shaft 42 is rotated about a ϕ axis. The θ rotation shaft 42 is rotatable thereon by 360 degrees or more. At this time, the length of the support shaft 12 and an arm of the bracket 46 is adjusted such that the center of the sphere 10 is positioned on the ϕ rotation shaft 44, whereby the sphere 10 can be rotated by an arbitrary angle at a focus position of the reference spherical surface 22. In this structure, to measure an area extending to a half of the sphere 10 by the laser interferometer 20, the sphere 10 is rotated about the θ rotation shaft 42 by 360 degrees and the ϕ rotation shaft 44 by 90 degrees from a position at which the support shaft 12 is orthogonal to the measurement optical axis to a position at which the support shaft 12 is parallel to the measurement optical axis.
FIGS. 3A and 3B show the relation among a measurable area by the apparatus with such a configuration, and the θ and ϕ rotation axes of the apparatus. In FIGS. 3A and 3B, the apparatus shown in FIG. 1 is viewed from above. First, the angle of the ϕ rotation shaft 44 at which the support shaft 12 is orthogonal to the measurement optical axis of the laser interferometer 20 is defined as a first support angle ϕ1. FIG. 3A shows this state. Defining a central axis of the support shaft 12 as a polar axis of the sphere 10, contours in the surface of the sphere 10 at positions orthogonal to the polar axis are considered as latitude lines of the sphere 10, and the contour having a maximum diameter is the equator (a first measurement latitude line). At the first support angle ϕ1, rotating the θ rotation shaft 42 directs an arbitrary point in the first measurement latitude line in the sphere 10 toward the laser interferometer 20. By performing measurement at the position, the shape of a single measurement area is measured at an arbitrary position of the θ rotation shaft 42. It is desirable that rotation intervals of the θ rotation shaft 42 be determined so as to have an overlapping area between the single measurement areas adjacent to each other, for the sake of a stitching operation performed afterward. This overlapping area may be approximately of the order of a half of a viewing angle of the laser interferometer 20, for example. Here, the first support angle ϕ1 is defined as a position at which the support shaft 12 is orthogonal to the measurement optical axis, but is not necessarily such a position and may be set at any arbitrary position.
Then, the ϕ rotation shaft 44 is rotated to set the support shaft 12 at a position different from the first support angle ϕ1. This position is referred to as a second support angle ϕ2. FIG. 3B shows this state. By rotating the θ rotation shaft 42 at this position, points on the spherical surface intersecting with the measurement optical axis of the laser interferometer 20 draw a trail. A contour line represented by this trail is referred to as a second measurement latitude line. Just as with an operation at the first support angle ϕ1, rotating the θ rotation shaft 42 allows measurement of the shape of the single measurement area at an arbitrary position of the θ rotation shaft 42 in the second measurement latitude line in the spherical surface. Just as with the rotation intervals of the θ rotation shaft 42, the distance between the first support angle ϕ1 and the second support angle ϕ2 may be approximately of the order of a half of the viewing angle of the laser interferometer 20, for example. A plurality of support angles ϕ are set in a rotation range of the ϕ rotation shaft 44, and the θ rotation shaft 42 is operated at each position. This procedure is performed until the single measurement areas corresponding to the individual positions cover a hemispherical part of the sphere 10. The shapes of a number of the single measurement areas obtained in this manner are stitched together by the stitching operation with reference to positional information of the θ rotation shaft 42 and the ϕ rotation shaft 44, to measure the surface shape of the sphere 10. The rotation range of the ϕ rotation shaft 44 is not limited to 90 degrees as shown in FIG. 2, and can be set in an arbitrary range as long as there is no physical contact between the laser interferometer 20 and the measurement position change mechanism 40, or the like. A necessary prerequisite for the plurality of single measurement areas covering the half of the sphere 10 is a rotation range of 90 degrees of the ϕ rotation shaft 44.
When the measurement position change mechanism 40 has a dimensional error, that is, each constituting part has a dimension different from a design value, or a movement error, the sphere 10 may be displaced from the focus position of the reference spherical surface 22 with rotation of the θ rotation shaft 42 and the ϕ rotation shaft 44. In the interferometer device for measuring the spherical surface, this positional displacement causes a measurement error. Accordingly, the apparatus of Non-Patent Literature 1 may be provided with, for example, three axes movement mechanism 48 having stages 48x, 48y, and 48z, as shown in FIG. 4. This positional displacement can be corrected by moving the sphere 10 with reference to an interference fringe image of the laser interferometer 20 so as to minimize the number of interference fringes.